Question

Use the image to answer the question.

An illustration shows a 3 D triangular prism. The side of the base is 4.5 centimeters. The perpendicular height of the triangular base is 3.9 centimeters. The perpendicular height of the lateral face from the apex to the center of the base is 3.5 centimeters. There are two right angle symbols to show the perpendicular lines. The heights are shown as dashed lines.

A metalworker is creating decorative points in the form of triangular pyramids to go on top of a fence she is building. She wants to know the surface area of each pyramid. Use the surface area formula to find the surface area of each pyramid based on the figure.

(1 point)
cm2
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Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the surface area of the pyramid, we need to find the area of each face and then add them together.

The base of the pyramid is a triangle with a side length of 4.5 cm and a height of 3.9 cm. The area of the base is (1/2) * base * height = (1/2) * 4.5 cm * 3.9 cm = 8.775 cm².

The lateral faces of the pyramid are three congruent triangles. The base of each triangle is the same as the base of the pyramid (4.5 cm), and the height of each triangle is 3.5 cm. The area of each lateral face is (1/2) * base * height = (1/2) * 4.5 cm * 3.5 cm = 7.875 cm².

There are three lateral faces, so the total area of the lateral faces is 3 * 7.875 cm² = 23.625 cm².

To find the surface area of the pyramid, we add the area of the base and the area of the lateral faces: 8.775 cm² + 23.625 cm² = 32.4 cm².

Therefore, the surface area of each pyramid is 32.4 cm².